#14261: Iwahori-Hecke algebra with several bases
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Reporter: brant | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: Iwahori Hecke | Merged in:
algebra | Reviewers: Andrew Mathas, Brant
Authors: Brant Jones, | Jones, Travis Scrimshaw
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #13735 #14014 |
#14678 #14516 |
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Comment (by nthiery):
Replying to [comment:34 andrew.mathas]:
> Here are a few other less important issues that I have come across:
> * I am confused by the `one_basis` method of all of the bases: why does
this return the identity element of the corresponding Coxeter group?
Initially I thought that this would return the identity element of the
Hecke algebra with respet to the current basis (which is implemented
as`T.one()`). If we really need a shorthand for the identity element of
the group shouldn't the method be called something like group_identity?
From the documentation of one_basis in AlgebrasWithBasis
(now in Algebras.Unital.WithBasis.ParentMethods.one_basis):
{{{
When the one of an algebra with basis is an element of
this basis, this optional method can return the index of
this element. This is used to provide a default
implementation of :meth:`.one`, and an optimized default
implementation of :meth:`.from_base_ring`.
}}}
So just a little standard shortcut which furthermore gives the system
a bit of information that can be used for some optimizations.
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:38>
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